This study presents the optimization of a two-degree-of-freedom landing gear model equipped with an inerter, aiming to reduce the peak displacement of the sprung mass under impulsive excitation typical of landing scenarios. The system is modeled as a mass–spring–damper augmented with an inerter, and the dynamic parameters are tuned using two optimization techniques: a gradient-based method (fmincon) and a Genetic Algorithm (GA). Both approaches successfully minimized the maximum vertical displacement of the airframe, with the gradient method converging faster and the GA demonstrating better robustness. The optimized configuration achieved a 52% reduction in peak displacement, along with enhanced damping, faster stabilization, and superior resilience under hard landings and stochastic disturbances. These results confirm the effectiveness of optimization in improving landing gear dynamics and suggest that hybrid methods may further enhance the design of high-performance aerospace suspensions.